Exercise $1\mathrm{.}21$ Explain the behavior of the sequence from the first problem in these notes using what you

know about how computers store numbers in double precision.

$x_{n+1}=\{\begin{array}{ccc}2x_n,& x_{n}in[0,& \frac{1}{2}]\\ [2x_n-1,& x_{n}in(\frac{1}{2},1]]\text{w}\text{i}\text{t}\text{h}& x_0=\frac{1}{10}\end{array}$

In particular, now that you know about how numbers are stored in a computer, how long do you expect it

to take until the truncation error creeps into the computation?